A Bayesian Functional Concurrent Zero-Inflated Dirichlet Multinomial Regression Model

Music City Center 

The human microbiome undergoes dynamic shifts in composition over time, exemplified by rapid changes in newborns or by shifts following dietary changes. Modeling the influence of exposures or treatments on microbial composition over time is essential to understanding the factors that drive these transitions. Often, Dirichlet-multinomial (DM) regression models are used to investigate the potential relation between observed covariates and microbial data due to its ability to accommodate potential overdispersion in and compositional structure of the data. However, traditional DM regression models are not equipped to handle repeated measures data, ignore potential zero-inflation that is characteristic of microbiome data, and assume the effect of a covariate is constant throughout the study period. Additionally, alternative methods for modeling longitudinal microbiome data often overlook the compositional structure of the data and time varying effects. To fill these gaps, we propose a functional concurrent zero-inflated Dirichlet-multinomial (FunC-ZIDM) regression model, which is designed to model time-varying relations between observed covariates and microbial taxa while accounting for zero-inflation, compositional structure, and repeated measures. Through simulation, we demonstrate the model's ability to estimate the relative abundance of compositional elements and to scale to large compositional spaces. We apply our model to investigate time-varying associations between infants' microbial composition and both breast milk intake and gestational age at birth during the 11-week postnatal period.